Solve 1/9-2+3/-frac{1{3}+2}

$$\frac{ \frac{ 1 }{ 9 } -2+3 }{ - \frac{ 1 }{ 3 } +2 }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

Convert 2 to fraction \frac{18}{9}.

$$\frac{\frac{1}{9}-\frac{18}{9}+3}{-\frac{1}{3}+2}$$

Since \frac{1}{9} and \frac{18}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1-18}{9}+3}{-\frac{1}{3}+2}$$

Subtract 18 from 1 to get -17.

$$\frac{-\frac{17}{9}+3}{-\frac{1}{3}+2}$$

Convert 3 to fraction \frac{27}{9}.

$$\frac{-\frac{17}{9}+\frac{27}{9}}{-\frac{1}{3}+2}$$

Since -\frac{17}{9} and \frac{27}{9} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-17+27}{9}}{-\frac{1}{3}+2}$$

Add -17 and 27 to get 10.

$$\frac{\frac{10}{9}}{-\frac{1}{3}+2}$$

Convert 2 to fraction \frac{6}{3}.

$$\frac{\frac{10}{9}}{-\frac{1}{3}+\frac{6}{3}}$$

Since -\frac{1}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10}{9}}{\frac{-1+6}{3}}$$

Add -1 and 6 to get 5.

$$\frac{\frac{10}{9}}{\frac{5}{3}}$$

Divide \frac{10}{9} by \frac{5}{3} by multiplying \frac{10}{9} by the reciprocal of \frac{5}{3}.

$$\frac{10}{9}\times \frac{3}{5}$$

Multiply \frac{10}{9} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{10\times 3}{9\times 5}$$

Do the multiplications in the fraction \frac{10\times 3}{9\times 5}.

$$\frac{30}{45}$$

Reduce the fraction \frac{30}{45} to lowest terms by extracting and canceling out 15.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$